Three-Port Reflectionless Down-Converter for Wideband and Multichannel Receiver With Flat Gain, Enhanced EVM, and High Stability

This article presents a three-port reflectionless down-converter to achieve flat gain, enhanced EVM, and high stability for wideband and multichannel receivers. The down-converter consists of a mixer with three reflectionless filters at IF, RF, and LO ports. The analysis of the proposed reflection model demonstrates that the elimination of reflected signals alleviates the problems of gain fluctuation and harmonics generation. Meanwhile, reflectionless operation effectively improves the dynamic range of the receiving system. To verify the mechanism and operation mentioned above, a series of reflectionless down-converters is designed and fabricated. The measurement results fully confirm the theoretical analysis, in which the three-port reflectionless converter supports a 300 MHz 256-QAM signal with an error vector magnitude (EVM) of 3.02%. The EVM of 400 MHz 64-QAM signal is below 4.50% when overlap bandwidth varies from 0 to 400 MHz. For an eight-carrier signal of 40 MHz 256-QAM, the proposed three-port reflectionless converter maintains the EVM difference among each channel lower than 0.15%.

To suppress the out-of-band mixing signals, filters are widely utilized in receivers.However, the stopband response of the conventional filter reflects a large amount of out-ofband signals to the system front-end and back-end.Such reflected signals generate additional intermodulation products at the nonlinear circuits (i.e., mixer), which lead to in-band and out-of-band interference.In-band interference is more destructive than out-of-band interference since it can overlap with the IF signal and degrade signal quality.Such occurrence of signal overlap deteriorates the receiver performance including error vector magnitude (EVM) and adjacent channel power ratio (ACPR).Recent studies have presented the reflectionless filter capable of reducing in-band interference by absorbing the out-of-band harmonics [12], [13], [14], [15], [16], [17], [18], [19].Since the reflectionless operation brings a clean in-band spectrum, the system-level reflectionless design for the receiver is significant.In [20] and [21], the reflection absorption technique in the IF or RF path is utilized to reduce intermodulation and improve the stability of the receiver.Meanwhile, the comparison of different mixing systems exhibits the improvement of reflectionless circuits on the dynamic range [22], [23].However, due to the absence of theoretical analysis and measurement comparison between conventional and reflectionless receivers, the merits of a reflectionless system are not fully manifested.The research of receivers with different reflectionless receiving paths (i.e., IF, RF, and LO paths) is meaningful but still deficient in recent work.Therefore, it is attractive to design a new reflectionless receiving architecture with enhanced performance.
Modern high-performance receivers employ more channels to extend the total spectrum bandwidth [24], [25], [26], [27].In a multichannel system, dynamic range and signal quality among channels are always different due to power fluctuation with frequency.Additional counter-balance components are required to compensate for the degraded gain for channels.Recent studies introduce independent gain control elements to maximize the dynamic range in receivers [28], [29], [30].However, in case the receiver operates in more complex carrier aggregation modes, the required number of control elements is exponentially increased.To fundamentally maintain the power balance of each channel, the gain fluctuation and harmonic interference induced by reflected signals are demanded to be eliminated.Therefore, it is critical to investigate and develop the channel-equalized receiver using reflection suppression technology to simplify the complex configuration with good signal quality.
A comparison of conventional and reflectionless receiver frameworks is shown in Fig. 1.The configuration of In this article, the theoretical analysis with circuit validation of a three-port reflectionless down-converter applied in wideband and multichannel receivers is proposed.First, a reflection model of the converter is introduced to analyze the effect of out-of-band reflected signals in the filtering and mixing process.Theoretical analysis demonstrates the influence of reflection behavior to gain fluctuation, linearity unbalance, harmonic generation, and system instability.Second, four converters are implemented to compare the effect of reflectionless operation in IF, RF, and LO paths.A comparison of analytical models and system-level measurements demonstrates the excellent accuracy of the reflection model.The proposed three-port reflectionless converter shows the 4.87 dB and 4.03 dBm reduction of gain difference and input third intercept point (IIP3) difference compared with the conventional converter.Besides, the three-port reflectionless converter achieves the EVM of 300 MHz 256-QAM with 3.02%.The EVM of 400 MHz 64-QAM is below 4.50% when the overlap bandwidth varies from 0 to 400 MHz.For an eight-carrier signal of 40 MHz 256-QAM, the EVM difference between channels is lower than 0.15%.This article is organized as follows.The prototype with principle and theoretical analysis of the reflectionless converter is discussed in Section II, while Section III presents the circuit implementation.In Section IV, the proposed reflectionless and conventional converters are fabricated, measured, and compared, which fully confirms the principle analysis.Besides, the comparison between four converters with different architectures is given.The conclusion is summarized in Section V.

II. REFLECTION MODEL ANALYSIS IN CONVERTERS
Fig. 2 shows the reflection model of the three-port converter.The IF, RF, and LO ports of the mixer are connected with three filters.Here, T IF , T RF , and T LO are the transmission function of such filters.The interconnects between devices are simplified as the ideal form with a constant impedance of Z 0 and three ports phases of θ 1 , θ 2 , and θ 3 .Meanwhile, the model gives the reflection coefficients of each port and the signal flow in the converter.In this section, the reflection model is used to analyze the influence of the reflection effect on the converter.
To clarify the reflectionless mechanism, a complete mathematical model is introduced to represent signal reflection in IF, RF, and LO paths, where the fluctuation of gain and linearity in a wideband system is analyzed.Besides, the system stability improvement by a reflectionless mechanism is demonstrated.Furthermore, in order to reveal the influence of gain fluctuation and harmonic interference on overall signal quality, the relationship between EVM and reflection coefficient is analyzed quantitatively.

A. Gain and Linearity Flatness Improvement by Reflectionless Operation
Mixer as a nonlinear part of the system, its frequency conversion characteristic is the main research object.Nevertheless, there still exist many nonideal factors that affect the mixing process.Generally, signal reflection associated with circuit mismatch always leads to a complex signal spectrum.In addition, signal leakage inevitably occurs between the three ports of the mixer, which interferes with the in-band signals.
In order to reveal the phenomenon of signal reflection and leakage, the linear transformation of the same frequency signals in the mixer is represented.Here, considering the incident and reflected signals in the mixing process, the scattering parameter of the mixer is introduced where S mix (ω) is a function of frequency.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.In the receiving link, the mixer is connected to filters.The magnitude of the reflection between the filter and mixer can be evaluated by the reflection coefficient.As shown in [31], the reflection coefficient is derived as (2 where 0 (ω) is the terminal reflection coefficient.Here, as a separate variable, θ reflects the interconnect length between devices.As a consequence, the reflection coefficient varies with operating frequency and connection phase.The reflection model of the three-port converter in Fig. 2 where α n (n = 1, 2, 3, . ..) is the nonlinearity coefficients of mixer.Fig. 3 exhibits the mixing model with reflective and reflectionless operations in the front-end and back-end of the mixer.As a nonlinear circuit, the mixer generates complex output products at the IF port.Therefore, the signals in the IF path consist of IF signal x IF (t) and other signals x ′ IF (t).The signal x ′ IF (t) consists of a complex spectrum with the expression as x iRF+ jLO (t) where i ̸ = 1 and j ̸ = −1 at the same time.
where S 21 and S 31 represent the signal leakage intensity and IF is the reflection coefficient at IF port.
After secondary reflection by RF and LO filters, the out-ofband mixing products x ′ RF (t) and x ′ LO (t) participate in the next mixing process with forward incident signals, which leads to the secondary mixing phenomenon as follows: The multiple mixing generates extra high-order harmonics, which messes up the spectrum.Meanwhile, the participation of reflected signals in mixing also affects the conversion gain of the mixer.Compared with the signal reflection in front part and back part illustrated in Fig. 3 In order to quantitatively research the effect of multiple mixing on the conversion gain, it is necessary to identify the practical signal components involved in the mixing process.Considering the dominant role of f RF and f LO in out-of-band reflected signals, other high-order mixing products can be ignored.Combined with [32], the conversion gain of converter is simplified as As shown in (7), the conversion gain of the IF signal is related to nonlinearity coefficients, scattering parameters, and reflection coefficients.In general, it is difficult to keep these parameters constant as frequency changes.As a result, the conventional converter shows a fluctuant gain in the wide frequency domain.Therefore, the multiple mixing of reflected signals deteriorates the gain flatness of the system.By contrast, in a reflectionless system, the gain of a reflectionless converter is perfectly stable as long as one of the following conditions is achieved: Thus, the amplitude fluctuation is well suppressed by a reflectionless system.Figs.4(a) and 5(a) exhibit the calculation results of normalized conversion gain of converter with different reflection coefficient and nonlinearity coefficient [34], [35], [36].The conversion gain curves in two conditions become flatter with reduced reflection coefficients.Meanwhile, it demonstrates that the gain fluctuation caused by reflection in the IF path is more drastic than that in the RF and LO paths.Therefore, it is valuable to implement reflectionless operation at the IF port with higher priority than the other two ports.
In order to analyze the nonlinear characteristic of the converter, two similar-frequency RF signals f RF1 and f RF2 are fed into the mixer.Generally, the third-order intermodulation signals f 2RF1−LO−RF2 is close to the IF signal of f RF1−LO , resulting in severe adjacent interference.The amplitude of the IM signal is derived with the equation in [32] as The IIP3 is obtained when the amplitude of the IM products becomes equal to that of the IF tones.Combining ( 7) and ( 9), the IIP3 is derived as Among these coefficients, the second and fourth harmonics α  Although the presence of reflected signals brings gain enhancement at some frequencies, it comes at the expense of gain fluctuation.Wideband signal inconsistency has a great influence on the overall performance of the system.Besides, the gain contribution caused by the reflected signal leads to the deterioration of linearity [21].The peak of the gain curve in Figs. 4 and 5 is exactly the valley of linearity curve.Please note that the highest gain and highest linearity can not be gotten simultaneously.In contrast, the reflectionless operation relaxes the tradeoff by maintaining stable gain and linearity within a wideband.Thus, the reflectionless receiver has the optimal gain and IIP3 combination in all frequency bands.
Furthermore, the influence of interconnection lines between devices in practical circuits can not be ignored.For conventional converters, the phase change of interconnect leads to the frequency shift of fluctuations.Fig. 6(a) and (c) shows the conversion gain with different interconnect phases.It shows the influence of the reflection coefficient and connection phases.Meanwhile, the IIP3 flatness is improved by inducing reflectionless operation at IF and RF/LO ports, as exhibited in Fig. 6(b) and (d).In summary, the phase shift of fluctuation caused by variable interconnect is well eliminated by reflectionless design.The reflectionless effects in the IF, RF, and LO paths make a significant contribution to gain and IIP3 flatness.
In addition, the stability of gain and linearity influences the flatness of the noise figure (NF).Due to the lack of reflected signal elimination, the harmonics entering the operating band worsen the NF of converters.Therefore, the NF fluctuation range of conventional converters is large.By contrast, the reflectionless effect can eliminate the noise generated by reflected signals and multimixing products.Thus, similar to gain and linearity, reflectionless converters achieve flatter NF.Nevertheless, the thermal noise introduced by resistors of reflectionless circuits cannot be ignored.For the proposed prototypes, the RF filter is in front of the mixer.Since the NF of a cascaded system is dominated by the noise characteristic of the first stage, the NF of the RF filter has a greater impact than that of the mixer and IF/LO filters.Therefore, the reflectionless converters have a slightly larger average NF than conventional ones.Note that by adding an LNA in front of the RF filter, the disadvantage of the average NF of reflectionless converters can be nearly ignored.

B. System Stability Improvement by Reflection Operation
To globally analyze the stability of the system, pole-zero identification is applied to the closed-loop transfer function [37], [38], [39].The pole-zero analysis can identify the unstable region according to specific circuit topology with suitable observation nodes.The system stability is analyzed by calculating the transfer function at both small and large signals.
Conventional scattering parameters are used to describe the electrical behavior of linear time-invariant two-port devices.Nevertheless, they cannot fully express the signal transfer process in a frequency conversion system.Therefore, the establishment of a transfer function related to each port of mixer is critical for stability analysis.
In the Appendix, the two-port scattering-parameter conversion matrix at [40] is extended to the three-port form by incorporating the LO port into the matrix.As a consequence, the electrical problem of multiple-frequency is transformed into equivalent single-frequency.In a three-port reflectionless system, the following relationship is expressed as: The reflection coefficient at the IF port of the mixer ( mix−IF ) can be derived according to [21].Using the condition in (11), mix−IF for a three-port reflectionless system is expressed as (12), shown at the bottom of the page.Since RF and LO In this case, the three-port reflectionless mixer achieves the requirement of unconditional stability.Fig. 7 shows the calculated reflection coefficient of a typical dual-gate FET mixer using the parameter extraction method in [34].Under the condition of small signal input, both the conventional and reflectionless receiver operate stably as shown in Fig. 7(a).However, once the input signal exceeds the upper boundary of the dynamic range, the conventional receivers inevitably reach the oscillation startup conditions.In this case, the circuit bias is influenced by the large input signal, while the receiver enters an abnormal operating statement.As shown in Fig. 7(b), the conventional architecture exists in an unstable region when the input signal enlarges, in which the reflection coefficient exceeds the value of 1.In contrast, reflectionless design keeps mix−IF , mix−RF , and mix−LO at zero up to 10 f 0 .Hence, the reflectionless operation in the receiver dramatically improves the system stability and dynamic range.

C. EVM and ACPR Enhancement of Wideband and Multichannel System by Reflection Operation
The multifunction receivers generally employ many carrier components to extend the total spectrum bandwidth.As described in the previous analysis, the multiple mixing of reflected signals affects the gain consistency, which is not dealt with in the multichannel system.The dynamic range and signal quality between channels are different due to the gain fluctuation and harmonics interference.The channel quality inconsistency greatly influences the demodulation process.The carrier aggregation technology achieves a constant passband interval between two adjacent channels f i CH and f j CH (i ̸ = j and i, j = 1, 2, 3, . ..), which are the i(th) and j(th) channels of multichannel signal.The mixing product of n(th) (n = 1, 2, 3, . ..) harmonics of the RF subchannel signal and m(th) (m = 1, 2, 3, . ..) harmonics of the LO signal fall into another subchannel when the relationship is satisfied as  (12) Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.The reflectionless operation alleviates the problems by suppressing the harmonics that interfere with the adjacent channels in multichannel systems.In the proposed reflection model, f RF and f LO as the main reflected signals affect the generation of high-order harmonics.Hence, the amplitude of harmonics can be derived as ) As shown in Fig. 8, the harmonic power enhances with the increase of reflection coefficients RF , LO , and IF .Therefore, harmonics are greatly suppressed by using circuits with low reflection characteristics.As shown in Fig. 1(b), the harmonic interference is noticeably suppressed with the reflectionless circuit.
EVM is a critical index, which provides quantitative assessments of receiver performance.Generally, EVM is degraded by numerous circuit nonidealities, including I/Q mismatch, gain flatness, LO leakage, intermodulation interference, amplitude nonlinearity, dc offsets, and frequency dependence [41], [42], [43], [44].Since the reflection brings gain fluctuation and intermodulation interference to the system, it is necessary to analyze the effect of the reflection coefficient on EVM.The gain imbalance of the in-band signal increases the amplitude error during demodulation.Here, the rms amplitude error influenced by gain flatness is derived as where f b is the bandwidth of the modulated signal and A IF and A sig are the amplitude of the practical input signal and ideal signal.Therefore, the EVM influenced by the gain imbalance can be expressed as Due to the influence of overlap between signal channel and intermodulation, the EVM considering in-band intermodulation interference is where A IM is the amplitude of intermodulation signal.
The total system EVM combined with the gain imbalance and intermodulation interference is calculated as Fig. 9 shows EVM gain−imbalance and EVM IM in 400 MHz and 64-QAM scenario.The calculated and simulated results show a good agreement, in which the two components of EVM gradually deteriorated with increased IF .In Fig. 10(a), EVM total is calculated by combining EVM gain−imbalance and EVM IM .Therefore, the demodulation error introduced by a gain imbalance in a wideband system is reduced with a lower reflection coefficient.Meanwhile, the influence of intermodulation interference to EVM IM in a multichannel system can be eliminated with the reflectionless circuit.ACPR represents the power ratio of the adjacent channel to the passband channel.The relationship between ACPR and reflection coefficient is analyzed with the calculation results of Fig. 8.And Fig. 10(b) shows the variation of ACPR versus IF , in which the harmonics of f 2LO−RF , f 3LO−RF , and f 3RF−2LO are adjacent channels.Therefore, the low reflection coefficient can suppress adjacent interference and decrease ACPR.In summary, The reflectionless design has important application value in wideband and multichannel communication systems.

III. CIRCUIT IMPLEMENTATION
To verify the mechanism mentioned above, four converters (i.e., a conventional and three reflectionless converters) are proposed.These converters consist of the same three-port wideband mixer with different IF, RF, and LO filters.Compared with conventional converters, the absorptive filters are introduced at different ports of the mixer for reflectionless converter design.Please note that the three-port reflectionless converter achieves reflectionless performance at all ports.Here, the proposed converters are implemented based on the printed circuit board (PCB) technology.Except for the Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.four fixed converters, the individual components including the mixer, filters, and transmission lines are fabricated.Conventional mixer achieves impedance matching only in the operation band.Due to the complexity of multiport circuits, wideband matching at all ports is rarely implemented in frequency conversion systems.Compared with conventional mixers, the reflectionless mixer pursues a much wider matching bandwidth, covering both passband and stopband.Meanwhile, the number of matching ports can be increased to obtain a better reflectionless effect.In order to achieve reflectionless operation, the matching bandwidth is at least two to three octaves of the passband to effectively absorb high-order harmonics in the stopband.
The traditional dual-gate mixer can implement a wide match at IF and RF ports but can not achieve the LO port match.Then, a three-port wideband matching mixer is proposed, as shown in Fig. 11(a).Compared with the dual-gate mixer, the proposed mixer adds an additional transistor M 3 at the bottom, which improves the match at the gate of transistor M 1 and M 2 .Utilizing the intrinsic matching capacity of common source topology, the mixer implements the wideband match at the IF and LO ports.Meanwhile, a distributed LC circuit at the RF port introduces a transmission pole to the matching network.Therefore, the reflectionless range is extended at the RF port.The GaAs FET ATF-54143 from Avago, high Q capacitors, resistors, and RF inductors from Murata are used to implement the single-ended mixer.The three ports of the mixer are matched in a broad frequency range simultaneously, as shown in Fig. 11(b).Measurement results show that the proposed mixer covers an ultra-wide matching range at IF and LO ports.Besides, the RF port exhibits a wide matching bandwidth to cover the f RF and f LO , which is sufficient to verify the reflectionless mechanism.
In order to achieve reflectionless operation in three paths of the converter, the lowpass prototypes in [22] are developed to implement absorptive filters, as shown in Fig. 12(a) and (b).Compared with the absorptive RF and LO filters, the absorptive IF filter demonstrates deeper stopband suppression by cascading two identical absorptive filters.In Fig. 12(c) and (d), the topology of inverse-chebyshev response is adopted to design conventional filters, which are optimized with similar S 21 and different S 11 compared with absorptive filters.With the involved components, various converter architectures can be achieved by combining different filters with the proposed three-port wideband matching mixer.Avoiding the repeatable verification, the four critical scenarios are implemented as exhibited in Fig. 13, in which RF frequency is varied from 0.1 to 2.4 GHz, LO frequency is from 0.1 to 1.6 GHz, and IF frequency is from 0 to 0.8 GHz.Converter 1 (i.e., the conventional type) is composed of the mixer and three conventional filters.By replacing the conventional filters of converter 1 with absorptive ones at different ports, the reflectionless operations in IF, RF, and LO paths are realized.In the fabricated circuits, converters 2 and 3 implement no reflection at the IF port and IF/RF paths, respectively.Meanwhile, converter 4 achieves the reflectionless operation in all paths (i.e., IF, RF, and LO).

IV. EXPERIMENTAL RESULTS
To verify the principle in Section II, the fabricated PCB circuits in Section III are measured using the setup shown in Fig. 14.Two signal sources and one spectrum analyzer are performed to measure the gain and linearity performance of converters.The signal source generates the modulation signal using the external baseband signal, which is provided by the arbitrary waveform generator (AWG).In order to measure the EVM and ACPR of the proposed converters, a spectrum analyzer with a demodulation function is used.Here, the LO power is −2 dBm for the measurement.

A. Flat Gain and Linearity With Reflectionless Mechanism
The conversion gain, IIP3, and OIP3 of the original mixer and four converters are compared in Fig. 15.The gain and linearity turn to flatter as the number of absorptive filters increases.In addition, the three-port reflectionless converter shows similar gain and linearity to the original mixer.The measurement results verify that the gain and linearity become flatter with reflectionless operation.The two-tone test of different converters is shown in Fig. 16, in which the output power of fundamental tone and third-order intermodulation distortion are measured with the change of input power.By choosing the conventional filters to connect the mixer,  as shown in Fig. 16(a), (c), and (e), OIP3 fluctuates with varied operating frequency.In contrast, OIP3 stabilizes at a constant level by replacing the conventional filter with reflectionless one, as shown in Fig. 16(b), (d), and (f).Therefore, the linearity flatness is significantly enhanced with the reflectionless operation at three ports of the mixer.Due to the influence of reflected signals, the conversion gain and linearity of conventional converters always fluctuate with variable interconnect between devices.As shown in Fig. 17, a 50 transmission line connects the mixer and filters in IF and LO paths, respectively.The gain and linearity fluctuations versus interconnection length are notable in conventional configuration.By contrast, the conversion gain and output 1 dB compression point (OP 1dB ) curves turn flatter by replacing the conventional filter with a reflectionless one.Therefore, the flat gain and linearity can be achieved with a reflectionless mechanism.
Fig. 18 shows the measured NF of four converters.Converter 1 introduces extremely large NF at certain frequencies.By contrast, converters 2, 3, and 4 exhibit flatter NF.Meanwhile, the average NF from 1.7 to 2.3 GHz of converter 4 is 1.1 dB larger than that of converter 1.Therefore, the reflectionless operation improves the flatness of NF with enhanced stability in a wide operation band, which verifies the previous analysis.

B. System Stability Enhancement With Reflectionless Mechanism
To verify the stability enhancement and harmonic suppression by reflectionless operation, the output spectrum of two converters is measured in Fig. 19.As exhibited in Fig. 19(a), at −15 dBm input power, the conventional converter generates a large number of in-band harmonics.Compared with conventional design, the three-port reflectionless converter well suppresses the harmonics under the same input power.Furthermore, once the input power raises to −5 dBm as shown   in Fig. 19(b), the conventional converter enters an unstable state and generates a mass of oscillations, which interferes the receiving spectrum.By contrast, the reflectionless converter always maintains a stable state and inhibits potential oscillations.Therefore, the proposed three-port reflectionless converter achieves a clean spectrum and enhances dynamic range.As described in Section II, a large input signal induces converters into an oscillation state, which is mostly produced by the port mismatch.Since the reflectionless design can achieve unconditional stability through wideband matching, the stability of the system is greatly improved.

C. EVM and ACPR Enhancement of Wideband and Multichannel System With Reflectionless Mechanism
In order to investigate the improvement of overall performance by reflectionless design, the measurement of EVM and ACPR between four converters is demanded.As shown in Fig. 20, four converters show different EVM performance in 100 MHz 64-QAM and 256-QAM scenarios.From converter 1 to converter 4, both the magnitude and fluctuation of EVM decrease as the number of absorptive filters increases.Compared to the other three converters, converter 4 with a three-port reflectionless design shows the lowest and flattest EVM.Fig. 21 exhibits the measured EVM and ACPR of converters with different connection lengths.In both the IF path and RF path, the EVM of conventional converters varies with connection length.By contrast, the reflectionless converters maintain a more stable EVM.Meanwhile, the same phenomenon is observed in ACPR, as shown in Fig. 21.Therefore, the reflectionless mechanism improves the stability of EVM and ACPR to interconnect variation.For the proposed mixer, the reflection coefficients of three ports are influenced by drain voltage V d1 .As a consequence, the reflection coefficients can be controlled by adjusting the bias voltage.As shown in Fig. 22(a), the harmonic f 2LO−RF overlaps with the IF signal.By reducing IF from 0.6 to 0.2, the ACPR of the converter drops off from −19.97 to −28.26 dBc.Fig. 22(b) shows a worsened ACPR with enlarged reflection coefficients, which are controlled by the bias voltage of the mixer.Thus, the reduction of reflection coefficients suppresses the adjacent interference.
To verify the advantage of the proposed three-port reflectionless converter, the wideband modulation signal measurement is performed on converters.Fig. 23 shows the measured output spectrum of two converters in the scenario of   −17.28 dBc in conventional converter, the three-port reflectionless converter exhibits better performance with EVM of 3.02% and ACPR of −28.10 dBc.Here, the passband signal of the reflectionless converter is obviously flatter than that of the conventional one.As shown in Fig. 24, under the input signal with 400 MHz bandwidth, 64-QAM, and 2.4 Gb/s data rate, once the third-order mixing product of the RF signal overlaps the IF signal by 150 MHz, the EVMs of two converters are 8.38% and 3.05%, respectively.Compared to conventional converter, the EVM of reflectionless one is less than 4.50% in the overlap bandwidth range from 0 to 400 MHz.Meanwhile, the ACPRs are −17.96and −27.66 dBc in conventional and three-port reflectionless converters, respectively.Thus, the proposed three-port reflectionless converter supports the wideband high-order modulation signal in a complex interference environment.
In order to compare the performance of two converters in a multichannel receiving scenario, the multiple-carrier signal tests are implemented in Fig. 25.The input nine-carrier signal has 450 MHz aggregate bandwidth with 256-QAM modulation in each channel.For conventional converters, the power of a single carrier varied with channel position.By contrast, channel power is consistent in the three-port reflectionless converter, as shown in Fig. 24(b).In addition, the reflectionless mechanism effectively restrains the in-band harmonics and enhances channel quality, such as the CH4 and CH9 marked in the figures.Next, the eight-carrier signal of 40 MHz 256-QAM for each channel is applied to two converters.Fig. 26 exhibits the measured output spectrum of converters.The maximum amplitude difference between channels of a conventional converter is 4.1 dBc, which is greatly reduced to only 0.7 dBc in a three-port reflectionless converter.Compared with the fluctuating channel quality of conventional converter, the EVMs of eight channels are basically maintained at around 2% in the reflectionless converter.Disturbed by high-order harmonics, the ACPR of a conventional converter rises to −9.9 dBc.With the same test condition, a three-port reflectionless converter decreases the ACPR to −25.6 dBc by effectively suppressing harmonics.
The performance summary and comparison of four converters (i.e., conventional, IF-port reflectionless, IF/RF-port reflectionless, and three-port reflectionless types) are shown in Table I.The proposed three-port reflectionless converter exhibits the best performance of gain flatness, linearity flatness, channel quality flatness, EVM, and ACPR.Therefore, the reflectionless operation with theoretical analysis investigated in this work is attractive for high-performance receivers.
V. CONCLUSION In this article, a down-converter with three-port absorptive operations is implemented for reflectionless receivers in wideband and multichannel systems.The analysis of the proposed reflection model exhibits characteristics of flat gain, improved linearity, harmonic suppression, and enhanced stability.Comparison between principle analysis and system-level measurement verifies the accuracy of the proposed reflection model.The measurement results of the three-port reflectionless converter support 300 MHz 256-QAM signal with EVM of 3.02%.The EVM of 400 MHz 64-QAM is less than 4.50%, covering the overlap bandwidth from 0 to 400 MHz.For an eight-carrier signal of 40 MHz 256-QAM in each channel, the proposed reflectionless converter maintains EVM difference between channels lower than 0.15%.With such good performance, such a reflectionless receiving architecture is attractive for the application of wideband high-order modulation and multiple-channel carrier aggregation technology.

APPENDIX
In order to analyze the signal conversion between the three ports of the mixer, the matrix of two-port scattering-parameter conversion in [40] In Fig. 27, the mixing model separates the ideal frequency-translating behavior of the mixer from its nonideal characteristic.The scattering-parameter matrix [S IF ] describes the nonideality of the mixer at its three ports by (20) with the same frequency ω IF .By combining the conversion matrix in (21), the nonideal conversion matrix of the mixer is defined.Similarly, the mixer is equivalent to the combination of ideal mixer with scattering-parameter matrix

Fig. 1 .
Fig. 1.Principle and configuration of (a) conventional heterodyne receiver and (b) proposed three-port reflectionless heterodyne receiver.conventional heterodyne receiver for wideband and multichannel systems is shown in Fig. 1(a).The filters remove the out-of-band signals (i.e., imaging signals, blockers, oscillator spur, and unwanted mixing products) to select useful signals.Due to the reflection characteristic of conventional filters, the spectrum is disturbed by adjacent interference of intermodulation and harmonic.Meanwhile, the gain fluctuation deteriorates the EVM.As a contrast, Fig. 1(b) exhibits the receiver prototype based on the three-port reflectionless down-converter.By absorbing the out-of-band signals in the receiving paths, harmonic interference and gain fluctuation are effectively eliminated.Therefore, the reflectionless receiver with a flat passband spectrum and enhanced signal quality is achieved, which is attractive for wideband and multichannel communication applications.In this article, the theoretical analysis with circuit validation of a three-port reflectionless down-converter applied in wideband and multichannel receivers is proposed.First, a reflection model of the converter is introduced to analyze the effect of out-of-band reflected signals in the filtering and mixing process.Theoretical analysis demonstrates the influence of reflection behavior to gain fluctuation, linearity unbalance, harmonic generation, and system instability.Second, four converters are implemented to compare the effect of reflectionless operation in IF, RF, and LO paths.A comparison of analytical models and system-level measurements demonstrates the excellent accuracy of the reflection model.The proposed three-port reflectionless converter shows the 4.87 dB and 4.03 dBm reduction of gain difference and input third intercept point (IIP3) difference compared with the conventional converter.Besides, the three-port reflectionless converter achieves the EVM of 300 MHz 256-QAM with 3.02%.The EVM of 400 MHz 64-QAM is below 4.50% when the overlap bandwidth varies from 0 to 400 MHz.For an eight-carrier signal of 40 MHz 256-QAM, the EVM difference between channels is lower than 0.15%.

Fig. 2 .
Fig. 2. Diagram of reflection model for a three-port converter.

Fig. 3 .
Fig. 3. Mixing model of IF path with (a) reflective operation and (b) reflectionless operation.Mixing model of RF and LO paths with (c) reflective operation and (d) reflectionless operation.
(a) and (c), the absorption of reflected signals in Fig. 3(b) and (d) suppresses the harmonics and maintains flat gain.

Fig. 4 .
Fig. 4. Calculation results of different reflection coefficients in the IF path without RF and LO filters.(a) Normalized conversion gain.(b) Normalized IIP3.

2 and α 4
are the key factors to IIP3.According to (10), IIP3 varies with frequency since the nonlinear coefficients and scattering parameters are the function of frequency.By contrast, IIP3 becomes flatter in reflectionless converter because reflection coefficient as zero eliminates two items of α 1 S 21 IF RF and α 1 S 31 IF LO .Therefore, the flatter linearity is obtained by reflectionless operation.The comparison of normalized IIP3 with different IF and α 2 /α 4 is exhibited in Fig. 4(b).Meanwhile, different reflection coefficients of RF and LO paths and nonlinearity coefficient ratios are combined to calculate the normalized IIP3 in Fig. 5(b).Compared with the unstable IIP3 of conventional converter, the reflectionless one decreases the fluctuation of linearity.Therefore, the gain and linearity flatness are improved simultaneously within a wide frequency range by reflectionless design.

Fig. 5 .
Fig. 5. Calculation results of different reflection coefficients in RF and LO paths without IF filter.(a) Normalized conversion gain.(b) Normalized IIP3.

Fig. 7 .
Fig. 7. Reflection coefficient of dual-gate FET mixer in the receiver with (a) small signal input and (b) large signal input.

Fig. 9 .
Fig. 9. Calculated and simulated (a) EVM gain−imbalance and (b) EVM IM versus reflection coefficient IF .As shown in Fig.1(a), the overlap of harmonics and in-band signals deteriorates the signal quality influences the channel flatness.The reflectionless operation alleviates the problems by suppressing the harmonics that interfere with the adjacent channels in multichannel systems.In the proposed reflection model, f RF and f LO as the main reflected signals affect the generation of high-order harmonics.Hence, the amplitude of harmonics can be derived as
Fig. 12(e), (f), and (g) compare the spectrum response of absorptive and conventional filters at RF, LO, and IF ports, which illustrate different out-of-band signal absorption abilities.

Fig. 17 .
Fig. 17.Measured results conversion gain and OP 1dB with different interconnection length θ : (a) IF filter and (b) LO filter ( f IF = 0.7 GHz and f LO = 1.5 GHz).

Fig. 21 .
Fig. 21.Measured results of EVM and ACPR in 100 MHz 256-QAM scenario with various connection lengths: (a) IF filter and (b) RF filter ( f IF = 0.7 GHz and f RF = 2.2 GHz).

Fig. 22 .
Fig. 22.(a) Measured results of spectrum with harmonic interference versus reflection coefficient.(b) ACPR and reflection coefficients with varied mixer drain voltage.

S 11 S
is expanded to a three-port prototype.The scattering-parameter matrix of the three-port device is expressed12 S 13 S 21 S 22 S 23 S 31 S 32 S 33 is a pure frequency translator among ω IF , ω RF , and ω LO , where the reflected wave coefficients b IF , b RF , and b LO are related to the incident wave coefficients a IF , a RF , and a LO by conversion matrix as follows: [S RF ] or [S LO ] at frequency ω RF or ω LO , respectively.Since [S IF ] = [S RF ] = [S LO], the scattering-parameter conversion matrix of the mixer is expressed as defines the incident and reflected signal flow, which are represented with the form of cosine functions.The x IF (t) = A IF cos ω IF t, x RF (t) = A RF cos ω RF t, and x LO (t) = A LO cos ω LO t,

TABLE I COMPARISON
OF FOUR CONVERTERS